This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 18.335 Mid-term Exam (Fall 2009) Problem 1: Caches and QR (30 pts) In class, we learned the Gram-Schmidt and modified Gram-Schmidt algorithms to form the (reduced) A = QR factorization of an m × n matrix A (with in- dependent columns a 1 ,a 2 ,... and n ≤ m ). In particular, for simplicity let us consider the computation of the m × n matrix Q only (whose columns are the orthonormal basis for the column space of A ), not worrying about keeping track of R , and for simplicity consider classical (not modified) Gram-Schmidt: q 1 = a 1 / k a 1 k for j = 2 , 3 ,...,n v j = a j- ∑ j- 1 i =1 q i ( q * i a j ) q j = v j / k v j k In this question, you will consider the cache complexity of this algorithm with an ideal cache of size Z (no cache lines). If the algorithm is implemented directly as written above, there is little temporal locality and Θ( mn 2 ) misses are required, independent of Z . You are also given that you can multiply an m × n matrix with an n × p matrix using Θ( mn +...
View Full Document
This note was uploaded on 09/26/2010 for the course MECHANICAL 2.001 taught by Professor Prof.carollivermore during the Spring '06 term at MIT.
- Spring '06